The Admissible Rules of ${{mathsf{BD}_{2}}}$ and ${mathsf{GSc}}$

Notre Dame Journal of Formal Logic 59 (3):325-353 (2018)
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Abstract

The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterize the existence of covers in certain models by means of formulae. Through this characterization, we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation, coupled with a description of a generalization of the disjunction property, to provide a basis of admissibility for the intermediate logics BD2 and GSc.

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10.1215/00294527-3838972

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References found in this work

A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Unification in intuitionistic logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
Proof theory for admissible rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.

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